FISHERY BULLETIN: VOL. 81, NO. 1 



Length-frequency analysis was chosen because 

 it could be applied to all samples, thus facili- 

 tating the comparison between samples. The use 

 of shell annuli is unreliable south of Cape Cod 

 (Mead and Barnes 1904; Shuster 1951), and 

 MacDonald and Thomas (1980) found little sup- 

 port for the technique in a Prince Edward Island 

 population. Constraints on the sampling design 

 precluded mark-recapture methods. 



For each population the modes on a length-fre- 

 quency histogram were broken down into a se- 

 ries of normal curves (Tesch 1971; MacDonald 

 and Pitcher 1979) by a Dupont 3 310 Curve Re- 

 solver, an analog computer which allows one to 

 break down a complex distribution into its basic 

 components in a graphical fashion (Appeldoorn 

 1981). From the resulting graphs the mean and 

 standard deviation of the curve which represents 

 each mode of the histogram can be obtained. The 

 curve resolver also determines the percentage of 

 the whole sample under each curve. 



Length-frequency analysis assumes that 

 spawning and settlement are discrete relative to 

 growth such that the length distributions of co- 

 horts are separable. Ropes and Stickney (1965), 

 Pfitzenmeyer (1962), and Brousseau (1978) found 

 that periods of both spawning and settlement of 

 each cohort were discrete events. In the latter 

 study, closely spaced cohorts within the same 

 year were separable by length-frequency analy- 

 sis using probability paper. In the present study, 

 discrimination of cohorts within a year class was 

 also possible. 



By inspection of the histograms and subse- 

 quent age-length curves and through considera- 

 tion of local recruitment processes and sampling 

 efficiency, ages were assigned to each cohort 

 (Brothers 1980; Schnute and Fournier 1980). 

 When possible, results were corroborated by 

 comparing them with previously published age- 

 length data for the same or nearby areas (e.g., 

 Belding 1930; Pfitzenmeyer 1972; Mead and 

 Barnes 1904; Gilfillan and Vandermuelen 1978; 

 Brousseau 1979), by comparison of adjacent 

 areas (e.g., the two Quonochontaug Pond sites), 

 by comparison of multiple samplings (Allen Har- 

 bor, Deer Isle), and by counts of shell annuli 

 (Portland, Deer Isle). 



The ages assigned were relative rather than 

 absolute; the time beyond the last yearly incre- 

 ment represents the fraction of expected yearly 



growth already obtained (Appeldoorn 1981). 

 This process results in a smoother growth curve, 

 since it linearizes seasonal growth variations 

 which would otherwise necessitate the use of a 

 more complex growth model (Cloern and Nichols 

 1978). 



The analysis of growth differences can be sim- 

 plified by comparing model parameters rather 

 than the direct age-length observations (Rao 

 1958). Growth was modeled by fitting the von 

 Bertalanffy growth function (VBGF) to the age- 

 length data. The VBGF is described by the equa- 

 tion: 



L, = U (1 



_ -ftt-to) 



3 Reference to trade names does not imply endorsement by 

 the National Marine Fisheries Service, NOAA. 



where t = time, L, = length at time t, L^ = maxi- 

 mum asymptotic length, K = growth constant, 

 and to = time when L, = 0. The single growth 

 parameter of Gallucci and Quinn ( 1979) is obtain- 

 ed by w = KL X . 



Recent studies on the statistical comparison of 

 VBGF's (Allen 1976; Bayley 1977; Gallucci and 

 Quinn 1979; Kimura 1980; Misra 1980; Kappen- 

 man 1981) and on the VBGF's biological basis 

 (Pauly 1979, 1981) have removed most of its past 

 criticism (Roff 1980). Dickie (1971) considered 

 the VBGF applicable for modeling population 

 growth even when individual growth did not fit 

 the model. The VBGF has been previously ap- 

 plied to Myo armaria by Munch-Petersen(1973), 

 Brousseau (1979), and Brethes and Desrosiers 

 (1981). 



The co parameter was chosen for analysis be- 

 cause, as a single parameter, it was easily calcu- 

 lated, tractable to further analysis, statistically 

 comparable, interpretable in both a biological 

 and statistical sense, and more robust than either 

 Kor L^ (Gallucci and Quinn 1979). A major bene- 

 fit of applying the VBGF is that only estimates of 

 length at known time intervals are required to 

 determine K, L tt , and hence co. Absolute age at 

 length is only required to estimate to. However, to 

 is of less importance here, since it is not a mea- 

 sure of growth, but only a location parameter. 



The VBGF was fitted to the data according to 

 the methods of Gallucci and Quinn (1979), using 

 the NLIN procedure of SAS79 (Helwig and 

 Council 1979) which yielded estimates of the 

 parameters, their asymptotic standard errors, 

 and the correlation coefficient of /f and L x . From 

 these estimates the co parameter and its variance 

 were calculated (Gallucci and Quinn 1979). The 

 regression procedure incorporated the size and 



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